Finite Group Databasebeta

← #23767066

Subgroups — #23767066

Order 10112.

780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579138C212yesmaximal, complemented
2C22×C22⋊Dic79C212yesmaximal
3#19098499C211yesmaximal, characteristic, complemented
4#19098486C212yesmaximal, complemented
5#19098475C211yesmaximal, characteristic, complemented
6#19098438C212yesmaximal, complemented
7#19098435C212yesmaximal, complemented
8#19098421C212yesmaximal, complemented
9#379×C79C211yesmaximal, characteristic
10C22×Dic158C2211yescharacteristic, complemented
11C23×Dic79C2212yes—
12C23×Dic79C2212yes—
13#14579138—28no—
14C2×C4⋊Dic79C2212yescomplemented
15C2×C4⋊Dic79C2211yescharacteristic, complemented
16C2×Dic79⋊C4C2212yescomplemented
17C2×Dic79⋊C4C2212yescomplemented
18C2×Dic79⋊C4C2212yescomplemented
19C2×C22⋊Dic79—28no—
20C2×C22⋊Dic79C2212yes—
21C2×C22⋊Dic79C2212yes—
22C2×C22⋊Dic79C2212yes—
23C2×C22⋊Dic79C2212yes—
24C79⋊#95C2211yescharacteristic, complemented
25C79⋊#95C2212yescomplemented
26C79⋊#95C2211yescharacteristic, complemented
27C79⋊#95C2212yescomplemented
28C25×C79C2211yescharacteristic
29C2×C22⋊C4×C79C2212yes—
30C2×C22⋊C4×C79C2212yes—
31C2×C22⋊C4×C79C2211yescharacteristic
32C2×C22⋊C4×C79C2211yescharacteristic
33C2×Dic158—24no—
34C2×Dic158—41no—
35C22×Dic79—24no—
36C22×Dic79—24no—
37C22×Dic79—24no—
38C22×Dic79—24no—
39C22×Dic79—42no—
40C22×Dic79—42no—
41C22×Dic79C2312yes—
42C22×Dic79C2312yes—
43C22×Dic79C2312yes—
44C22×Dic79C2312yes—
45C4⋊Dic79—24no—
46C4⋊Dic79—41no—
47Dic79⋊C4—24no—
48Dic79⋊C4—24no—
49Dic79⋊C4—42no—
50C22⋊Dic79—24no—
51C22⋊Dic79—24no—
52C22⋊Dic79—24no—
53C22⋊Dic79D418yes—
54C24×C79—24no—
55C24×C79—24no—
56C24×C79—41no—
57C24×C79—41no—
58C24×C79Q814yescomplemented
59C24×C79C2311yescharacteristic
60C24×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2312yes—
64C22⋊C4×C79—24no—
65C22⋊C4×C79—24no—
66C22⋊C4×C79—41no—
67C22⋊C4×C79—41no—
68C23×C79—22no—
69C23×C79—22no—
70C23×C79—22no—
71C23×C79—22no—
72C23×C79—216no—
73C23×C79—22no—
74C23×C79—22no—
75C23×C79—21no—
76C23×C79—21no—
77C23×C79—44no—
78C23×C79—44no—
79C23×C79—48no—
80C23×C79—44no—
81C23×C79C2×D414yes—
82C23×C79C2×Q812yes—
83C23×C79C2×Q814yes—
84C23×C79#4114yes—
85C23×C79C2411yescharacteristic
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79—22no—
90C2×C4×C79—22no—
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79—22no—
102C2×Dic79—22no—
103C2×Dic79—48no—
104C2×Dic79—48no—
105C2×Dic79C2×D414yes—
106C2×Dic79C2×D414yes—
107Dic158—44no—
108C22×C79—24no—
109C22×C79—24no—
110C22×C79—24no—
111C22×C79—24no—
112C22×C79—24no—
113C22×C79—24no—
114C22×C79—24no—
115C22×C79—22no—
116C22×C79—416no—
117C22×C79—41no—
118C22×C79—42no—
119C22×C79—41no—
120C22×C79C22⋊Q818yescomplemented
121C22×C79C22×D412yes—
122C22×C79C22×Q811yescharacteristic
123C22×C79C2×#4112yes—
124C22×C79H(5,𝔽2)11yescharacteristic
125C22×C79H(5,𝔽2)11yescharacteristic
126C4×C79—41no—
127C4×C79—42no—
128C4×C79—41no—
129Dic79—24no—
130Dic79—24no—
131Dic79—42no—
132Dic79—42no—
133C2×C79—28no—
134C2×C79—42no—
135C2×C79C2×C22⋊Q812yes—
136C2×C79#54311yescharacteristic
137C2×C79D4211yescharacteristic
138C2×C79#54612yes—
139C2×C79#55111yescharacteristic
140#2437—791nomaximal, Sylow
141C79#243711yescharacteristic, complemented, Sylow
142C2×C22⋊Q8—792no—
143C22×C22⋊C4—792no—
144#399—791no—
145#396—792no—
146#393—791no—
147#385—792no—
148#385—792no—
149#380—792no—
150#379D7911yescharacteristic
151C25C2×D7911yescharacteristic
152C22×Q8—791no—
153C23×C4—792no—
154C23×C4—792no—
155C22⋊Q8—1588no—
156C2×C4⋊C4—792no—
157C2×C4⋊C4—791no—
158C2×C4⋊C4—792no—
159C2×C4⋊C4—792no—
160C2×C4⋊C4—792no—
161C2×C22⋊C4—792no—
162C2×C22⋊C4—792no—
163C2×C22⋊C4—792no—
164C2×C22⋊C4—792no—
165C2×C22⋊C4—1588no—
166C2×C22⋊C4C2×D7912yes—
167C2×C22⋊C4C2×D7912yes—
168C2×C22⋊C4C2×D7911yescharacteristic
169C2×C22⋊C4C2×D7911yescharacteristic
170#95—791no—
171#95—792no—
172#95—792no—
173#95—791no—
174C24—24no—
175C24—24no—
176C24—41no—
177C24—41no—
178C24Dic15814yescomplemented
179C24C22×D7911yescharacteristic
180C24C22×D7912yes—
181C2×Q8—3161no—
182C2×Q8—1584no—
183C22×C4—3162no—
184C22×C4—3162no—
185C22×C4—792no—
186C22×C4—792no—
187C22×C4—792no—
188C22×C4—792no—
189C22×C4—1584no—
190C22×C4—1584no—
191C22×C4—1584no—
192C22×C4—1584no—
193C22×C4C22×D7911yescharacteristic
194C22×C4C22×D7912yes—
195C22×C4C22×D7911yescharacteristic
196C4⋊C4—3162no—
197C4⋊C4—3161no—
198C4⋊C4—1584no—
199C4⋊C4—1584no—
200C4⋊C4—1584no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—798no—
206C22⋊C4—1584no—
207C22⋊C4—1584no—
208C22⋊C4—1584no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—21no—
215C23—21no—
216C23—216no—
217C23—22no—
218C23—44no—
219C23—44no—
220C23—48no—
221C23—44no—
222C23D4×D7914yes—
223C23C2×Dic15812yes—
224C23C2×Dic15814yes—
225C23#1192962314yes—
226C23C23×D7911yescharacteristic
227Q8—3164no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—3168no—
236C2×C4—3168no—
237C2×C4—794no—
238C2×C4—794no—
239C2×C4—1582no—
240C2×C4—1582no—
241C2×C4—1582no—
242C2×C4—1582no—
243C2×C4—1582no—
244C2×C4—1582no—
245C2×C4—1582no—
246C2×C4—1582no—
247C2×C4—1582no—
248C2×C4—1582no—
249C22—24no—
250C22—24no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—22no—
256C22—24no—
257C22—416no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22#1457913818yescomplemented
262C22C2×D4×D7912yes—
263C22C22×Dic15811yescharacteristic
264C22C2×#1192962312yes—
265C22#1457920611yescharacteristic
266C22#1457920611yescharacteristic
267C4—41no—
268C4—42no—
269C4—41no—
270C4—3162no—
271C4—3162no—
272C4—1584no—
273C4—1584no—
274C2—28no—
275C2—42no—
276C2C2×#1457913812yes—
277C2#1909918911yescharacteristic
278C2#1909919511yescharacteristic
279C2#1909920012yes—
280C2#1909924411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#379×C79C2
prime radicalC25×C79C22
hypercenter#379D79
hypocenterC79#2437
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #379

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14579138C2semidirect
3. #19098499C2semidirect
4. #19098486C2semidirect
5. #19098475C2semidirect
6. #19098438C2semidirect
7. #19098435C2semidirect
8. #19098421C2semidirect
10. C22×Dic158C22semidirect
14. C2×C4⋊Dic79C22semidirect
15. C2×C4⋊Dic79C22semidirect
16. C2×Dic79⋊C4C22semidirect
17. C2×Dic79⋊C4C22semidirect
18. C2×Dic79⋊C4C22semidirect
24. C79⋊#95C22semidirect
25. C79⋊#95C22semidirect
26. C79⋊#95C22semidirect
27. C79⋊#95C22semidirect
58. C24×C79Q8semidirect
120. C22×C79C22⋊Q8semidirect
141. C79#2437semidirect
178. C24Dic158semidirect
261. C22#14579138semidirect